I have listed the information I am working off of (6) and I could really use help on Exercise 1 and 2!

Thank you!

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R(t):=12(1)= VX (r)]? + [Y (1)]2. Newton's inverse square law then states that K2 2+ Z=0 1232 (6) where 2 denotes the second derivative and [16, 14, Eq. (14.2), p. 39] K = 2+(M+m) with k representing the universal gravitational constant and M and m the masses of the two bodies. The purpose of the following exercises consists in developing changes of both spatial (Z) and temporal (1) coordi- nates to eliminate the singularity of the differential equation (6) at the origin, where Z=0. Exercise 1 Verify that if a solution curve Z never passes through the origin, then o has an inverse function defined on the whole real line. Exercise 2 Establish an integral formula for the inverse function, t=0-1. In particular, find a formula for the derivative of t. R(t):=12(1)= VX (r)]? + [Y (1)]2. Newton's inverse square law then states that K2 2+ Z=0 1232 (6) where 2 denotes the second derivative and [16, 14, Eq. (14.2), p. 39] K = 2+(M+m) with k representing the universal gravitational constant and M and m the masses of the two bodies. The purpose of the following exercises consists in developing changes of both spatial (Z) and temporal (1) coordi- nates to eliminate the singularity of the differential equation (6) at the origin, where Z=0. Exercise 1 Verify that if a solution curve Z never passes through the origin, then o has an inverse function defined on the whole real line. Exercise 2 Establish an integral formula for the inverse function, t=0-1. In particular, find a formula for the derivative of t